Biometrical Letters

ISSN:1896-3811

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Volume 49 Number 2 pp. 159-175

Zofia Hanusz 1, Joanna Tarasińska 1, Zbigniew Osypiuk 1

1Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-934Lublin, Poland

On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality

Summary

The kurtosis-based tests of Mardia and Srivastava for assessing multivariate normality (MVN) are considered. The asymptotic standard normal distribution of their test statistics, under normality, is often misused for too small samples. The purpose of this paper is to suggest mean-and-variance corrected versions of the Mardia and Srivastava test statistics. Simulation studies evaluating both the true sizes and the powers of original and corrected tests against selected alternatives are presented and compared to the size and the power of the Henze-Zirkler test. The proposed corrected statistics have empirical sizes closer to a nominal significance level than the original ones. It is also shown that the corrected versions of the tests can be more powerful than the original ones.

Keywords: Henze-Zirkler test, true size studies, power studies, heavy-tailed distributions, light-tailed distributions
https://content.sciendo.com/downloadpdf/journals/bile/49/2/article-p159.pdf Full text available in Adobe Acrobat format

DOI: 10.2478/bile-2013-0012

For citation:

MLA Hanusz, Zofia, et al. "On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality." Biometrical Letters 49.2 (2012): 159-175. DOI: 10.2478/bile-2013-0012
APA Hanusz, Z., Tarasińska, J., & Osypiuk, Z. (2012). On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality. Biometrical Letters 49(2), 159-175 DOI: 10.2478/bile-2013-0012
ISO 690 HANUSZ, Zofia, TARASIńSKA, Joanna, OSYPIUK, Zbigniew. On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality. Biometrical Letters, 2012, 49.2: 159-175. DOI: 10.2478/bile-2013-0012